Neuromathematics of Vision (Paperback, Softcover reprint of the original 1st ed. 2014)

Giovanna Citti, Alessandro Sarti

Series: Lecture Notes in Morphogenesis

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This book is devoted to the study of the functional architecture of
the visual cortex. Its geometrical structure is the differential
geometry of the connectivity between neural cells. This
connectivity is building and shaping the hidden brain structures
underlying visual perception. The story of the problem runs over
the last 30 years, since the discovery of Hubel and Wiesel of the
modular structure of the primary visual cortex, and slowly cams
towards a theoretical understanding of the experimental data on
what we now know as functional architecture of the primary visual
cortex.Experimental data comes from several domains:
neurophysiology, phenomenology of perception and neurocognitive
imaging. Imaging techniques like functional MRI and diffusion
tensor MRI allow to deepen the study of cortical structures. Due to
this variety of experimental data, neuromathematematics deals with
modelling both cortical structures and perceptual spaces.From the
mathematical point of view, neuromathematical call for new
instruments of pure mathematics: sub-Riemannian geometry models
horizontal connectivity, harmonic analysis in non commutative
groups allows to understand pinwheels structure, as well as
non-linear dimensionality reduction is at the base of many neural
morphologies and possibly of the emergence of perceptual units. But
at the center of the neurogeometry is the problem of harmonizing
contemporary mathematical instruments with neurophysiological
findings and phenomenological experiments in an unitary science of
vision.The contributions to this book come from the very founders
of the discipline.